Answer
Converges
Work Step by Step
We will apply the limit comparison test with $a_n=\Sigma_{n=1}^{\infty} \dfrac{1}{(n+1)^3}$ and $b_n=\Sigma_{n=1}^{\infty} \dfrac{1}{n^2}$
We can see that the series $\Sigma b_n$ shows a convergent p-series with $p=2 \gt 1$.
Next, we have $\lim\limits_{n \to \infty} \dfrac{a_n}{b_n} =\lim\limits_{n \to \infty} [\dfrac{\dfrac{1}{(n+1)^3}}{1/n^2}]$
or, $=\lim\limits_{n \to \infty} \dfrac{1/n }{(1+1/n)^3}$
or, $=0$
Hence, we can see that the given series converges by the limit comparison test.
